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Mind Games

Posted Mar 24,2009

Lawrence Weinstein doesn’t
know how many jelly beans
are in this jar, but he has
a very good guess. And it’s
higher than you might expect.
Weinstein, who teaches
estimation at Virginia’s Old
Dominion University, has a
knack for solving problems
with little data. His secret
is more method than magic:
Break questions into pieces,
approximate, and use metric
units for easier math.

Fermi estimation, as such
a method is known, helps
experts decide if problems—
from jelly bean counts to
carbon counts—warrant further
calculation. Precision isn’t
always necessary. Take sea
level rise. By assuming the
thickness of the Antarctic
ice sheet (1,000 meters) and
dividing that by how many
Antarcticas he thought would
cover the Earth (30), Weinstein
surmised that melting ice
caps could raise sea levels at
least 30 meters. Though USGS
reports suggest a 73-meter rise
(80 meters if you include Greenland’s
ice sheet), his rough
guess still predicts catastrophe.
“I don’t need to refine that
number,” says Weinstein. “I’m
in Virginia Beach. Either way,
I’m underwater.” —Oliver Uberti

ANYONE’S GUESS You don’t
have to split atoms to guess how
many jelly beans are in this jar.
Simply break the problem into steps.

1 Approximate the jar’s radius (r) in beans. (Hint: Count the jar's width, then divide by two.)2 Estimate its height (h) in beans.
3 Use these numbers to figure the
jar’s occupied volume: V = πr2 x h.
Round π off to three.
4 Gloat (Put your mouse over the jar photo and wait for the answer.)

Comments

Richard, I hand-counted all 4,466 jelly beans. It took over two hours on a sad Thursday night. But before I did that, I followed Weinstein's estimation formula. I used a radius of 7 and a height of 30. So in V = (pi)r^2 * h, I figured a volume of (3)(7*7) * 30 = roughly 4500. A difference of only 34 beans!

In Fermi estimation, scientists are not looking for precision; they just want to be in the ballpark. Says John A. Adam, professor of mathematics at Old Dominion University, "if the “method” gives a correct answer to within a factor of two, that’s pretty good."

**Remember to count the jar's radius (half the width) instead of its diameter.